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Lorico [155]
4 years ago
5

The area of a rectangle is 99 ft^2, and the length of the rectangle is 7 more than double the width. Find the dimensions of the

rectangle.
Mathematics
1 answer:
Sergio039 [100]4 years ago
7 0

Answer:

width =5.5ft

length =18

Step-by-step explanation:

w=x

L=2x+7

area=w*L

99 = x(2x+7)

99=2x^{2} +7x

2x^{2} +7x-99=0

2x^{2} +18x-11x-99=0

2x(x+9)-11(x+9)=0

(2x-11)(x+9)=0

2x-11=0

2x=11

x=11/2

x=5.5

L=2x+7=2*5.5+7=11+7=18

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which equation represents an exponential function that passes through the point (2, 80)? f(x) = 4(x)5 f(x) = 5(x)4 f(x) = 4(5)x
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we know that

if the exponential function passes through the given point, then the point must satisfy the equation of the exponential function

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<u>case A</u>  f(x)=4(x^{5})

For x=2 calculate the value of y in the equation and then compare with the y-coordinate of the point

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therefore

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<u>case B</u>  f(x)=5(x^{4})

For x=2 calculate the value of y in the equation and then compare with the y-coordinate of the point

so

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the exponential function f(x)=5(x^{4}) passes through the point (2,80)

<u>case C</u>  f(x)=4(5^{x})

For x=2 calculate the value of y in the equation and then compare with the y-coordinate of the point

so

f(2)=4(5^{2})=100

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therefore

the exponential function f(x)=4(5^{x}) not passes through the point (2,80)

<u>case D</u>  f(x)=5(4^{x})

For x=2 calculate the value of y in the equation and then compare with the y-coordinate of the point

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therefore

the exponential function f(x)=5(4^{x}) passes through the point (2,80)

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<u>the answer is</u>

f(x)=5(x^{4})

f(x)=5(4^{x})

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